Summary: Optimistic Shannon Coding Theorems for Arbitrary
Single­User Systems \Lambda
Po­Ning Chen y and Fady Alajaji z
y Department of Communication Engineering
National Chiao­Tung University
HsinChu, Taiwan, R.O.C.
z Department of Mathematics and Statistics
Queen's University
Kingston, Ontario K7L 3N6, Canada
Abstract
The conventional definitions of the source coding rate and of channel capacity re­
quire the existence of reliable codes for all sufficiently large blocklengths. Alternatively,
if it is required that good codes exist for infinitely many blocklengths, then optimistic
definitions of source coding rate and channel capacity are obtained.
In this work, formulas for the optimistic minimum achievable fixed­length source
coding rate and the minimum ''­achievable source coding rate for arbitrary finite­
alphabet sources are established. The expressions for the optimistic capacity and the
optimistic ''­capacity of arbitrary single­user channels are also provided. The expres­
sions of the optimistic source coding rate and capacity are examined for the class of
information stable sources and channels, respectively. Finally, examples for the com­